On the asymptotic Plateau problem for CMC hypersurfaces in hyperbolic space

2015/03/27 by Jaime Ripoll, Ripoll, Jaime, Miriam Telichevesky +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1503.08083

openalex publication_date 2015/03/27 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Let ℝ₊ⁿ⁺¹ be the half-space model of the hyperbolic space ℍⁿ⁺¹. It is proved that if Γ⊂\ x_n+1=0\ ⊂∂_∞ℍⁿ⁺¹ is a bounded C⁰ Euclidean graph over \ x₁=0, x_n+1=0\ then, given \vert H\vert <1, there is a complete, properly embedded, CMC H hypersurface Σ of ℍⁿ⁺¹ such that ∂_∞ S=Γ∪\ x_n+1=+∞\ . This result can be seen as a limit case of the existence theorem proved by B. Guan and J. Spruck in \citeGS on CMC \vert H\vert <1 radial graphs with prescribed C⁰ asymptotic boundary data.

Related

• On the asymptotic Plateau's problem for CMC hypersurfaces in hyperbolic\n space
• On the asymptotic Plateau problem in hyperbolic space
• Curvature estimates for semi-convex solutions of asymptotic Plateau problem in ℍⁿ⁺¹
• Smooth Solutions to Asymptotic Plateau Type Problem in Hyperbolic Space
• On the asymptotic Plateau's problem for CMC hypersurfaces on rank 1\n symmetric spaces of noncompact type